A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball (Use π= 22/7)
Answers
Given : Radius of a cylindrical tube (R) = 12 cm
Level of water raised in the cylindrical tube (h) = 6.75 cm
Let ‘r’ be the radius of the spherical ball.
Volume of water raised in the cylindrical tube is equal to the volume of the spherical ball.
Volume of water raised in the cylindrical tube = Volume of spherical ball
πR²h = 4/3πr³
R²h = 4/3r³
12² × 6.75 = 4/3 r³
r³ = (12 × 12 × 6.75 × 3) / 4
r³ = (3 × 12 × 6.75 × 3)
r³ = 729
r = ³√729 = 9
r = 9 cm
Hence, the radius of the spherical ball is 9 cm.
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Answer:
Step-by-step explanation:
πR²h = 4/3πr³
R²h = 4/3r³
12² × 6.75 = 4/3 r³
r³ = (12 × 12 × 6.75 × 3) / 4
r³ = (3 × 12 × 6.75 × 3)
r³ = 729
r = ³√729 = 9
r = 9 cm